Tìm giới hạn \(B = \mathop {\lim \to 0} \;2x - \cos {\sin \;3x\; - \sin \;4x\;}

* Hướng dẫn giải

\(\begin{array}{l}
B = \mathop {\lim }\limits_{x \to 0} \frac{{\cos \;2x - \cos \;3x}}{{x\left( {\sin \;3x\; - \sin \;4x\;} \right)}} = \mathop {\lim }\limits_{x \to 0} \frac{{2\sin \frac{{5x}}{2}\sin \frac{x}{2}}}{{ - 2x\cos \frac{{7x}}{2}\sin \frac{x}{2}}}\\
 =  - \mathop {\lim }\limits_{x \to 0} \left( {\frac{5}{2}.\frac{{\sin \frac{{5x}}{2}}}{{\frac{{5x}}{2}}}} \right).\mathop {\lim }\limits_{x \to 0} \frac{1}{{\cos \frac{{7x}}{2}}} = \frac{5}{2}
\end{array}\)